PSAT Math Multiple-Choice Question 422: Answer and Explanation

Question: 422

A book publisher pays writers a base fee of $2,500 for each book that it publishes, plus 5 cents per word. If one of its writers earned $8,000 on her book last year, how many words, w, did she write for the publisher?

• A. 11,000
• B. 110,000
• C. 155,000
• D. 250,000

Correct Answer: B

Explanation:

B

Difficulty: Easy

Getting to the Answer: First, figure out the function that will show you how the magazine publisher pays its writers. The writers earn $2,500 plus $0.05 per word. So the function for earnings, E, is: E(w) = $2,500 + $0.05(w).

Plug in what you know and solve for what you don't. The writer made $8,000 for writing one book, so $8,000 = $2,500 + .05(w). Solve for w:

$8,000 = $2,500 + $0.05(w)

$5,500 = $0.05(w)

w = 110,000

So to earn $8,000, the writer wrote 110,000 words for the publishing company. That matches (B).